Using the 2016 Transit of Mercury to
Find the Distance to the Sun
Jay M. Pasachoff, Williams College, Williamstown, MA, and Caltech, Pasadena, CA
Bernd Gährken, Bavarian Public Observatory, Munich, Germany
Glenn Schneider, Steward Observatory, The University of Arizona, Tucson, AZ
T
he May 9, 2016, transit of Mercury was observed simultaneously from the Big Bear Solar Observatory
in California and from a site in Germany. From the
measured displacement between the views from the two sites
of Mercury’s disk silhouetted against the solar granulation, we
were able to calculate the distance to the Sun in linear units
(kilometers), not merely the proportionality given by Kepler’s
third law.
When, in 1618, Johannes Kepler in his Harmony of the
World established the relation between the distances and
orbital periods of the known planets as they orbit the Sun,
our basic knowledge of the clockwork of the solar system was
set.1,2 But all those distances were relative, with the square of
the orbital periods being proportional to the cube of the distances (technically, the lengths of the semimajor axes of the
orbital ellipses that Kepler had advanced in his first law, from
1609).3 The absolute calibration of the distance scale of the solar system (e.g., in physical units such as kilometers), however,
remained unknown.
Kepler’s Rudolphine Tables of 1627 predicted transits of
Mercury and Venus across the face of the Sun in 1631, after Kepler had died. When Mercury’s transit was seen, that
validated not only Kepler’s laws but even the Copernican
heliocentric theory of planetary motion.4 The 1631 transit of
Venus was not seen in Europe. But a young scientist, Jeremiah
Horrocks, restudied Kepler’s tables and realized that there
would be a transit of Venus in 1639. Only he and one correspondent of his then saw it.5
Transits of Venus are rare: they occur in pairs separated by
eight years, with then gaps of 105.5 or 121.5 years. So there
were transits in 1761 (famously observed by Captain Cook
from Tahiti) and 1769 and 1874 and 1882. No transits of
Venus were visible from Earth in the 20th century; we have
recently had a pair in 2004 and 2012.6,7 Transits of Mercury
appear more often; the first was seen in 1631 by Gallendi and
provided early confirmation of the accuracy of Kepler’s tables.
In the 21st century, there have been transits of Mercury in
2003, 2006, 2016, and after the next, on Nov. 11, 2019, there
will be 10 more.8
In 1715, Edmond Halley figured out a method of finding
the distance to the Sun by having observers time a transit of
Venus from distances far apart from each other—in his recommendation, as far north and as far south as possible. (The
predictions were not sufficiently accurate for transits of Mercury to attempt the same.) But his method required timing the
entry of Venus’s silhouette onto the Sun and its exit, so-called
second and third contacts, to about one second of time.
It turned out that the “black-drop effect,” a non-clean
separation of Venus’s silhouette from the solar edge, reduced
the discernable time resolution to about one minute, preventing an accurate determination of the solar distance. Two of us
(JMP and GS) used spacecraft observations of a 1999 transit
of Mercury to finally explain the true cause of the black-drop
effect, which is a composite effect related to the finite resolution of the telescope and the extreme drop-off in brightness at
the edge of the Sun, which, after all, is gaseous and so has no
sharp edge.9,10
In this article, we describe our use of simultaneous observations of the 2016 transit of Mercury made from two widely
separated locations on Earth to determine the distance to the
Sun in a way different from that suggested in 1715 by Halley. Using an internet link, teachers and students can make a
similar derivation at the 2019 transit of Mercury also based
on parallax and requiring only a set of measurements at one
agreed-upon instant of time. We did not compare timing of
the contacts (Halley’s method), which groups did for the 2012
transit of Venus.11
The current observations
As with transits of Venus, transits of Mercury can also be
used to determine the astronomical unit (au), which is a measure of the average distance of Earth from the Sun. Historically, however, such measurements have not been made with
transits of Mercury since that planet is much smaller and farther away, giving a much lower expected accuracy. Measuring
the astronomical unit from the transit of Mercury was one of
the planned experiments for the May 9, 2016, transit.
One of us (BG) organized a worldwide volunteer effort to
try to compare measurements of the May 9, 2016, transit of
Mercury from pairs of widely separated sites on Earth. Up to
Fig. 1. A reprocessed image of the transit of Mercury of May 9,
2016, taken with a 9-cm Questar telescope and Questar filter.
Note that round Mercury (lower right) is smaller even than a
small-size sunspot group.
THE PHYSICS TEACHER ◆ Vol. 55, M ARCH 2017
137
(a)
(b)
(c)
Fig. 2. The Big Bear Solar Observatory with its six-year-old New Solar Telescope, a 1.6-m off-axis reflector, is on a small
artificial island in Big Bear Lake, California. (a) Author JMP is shown in front of the telescope’s dome. (b) The Sun’s concentrated beam is so hot that most of it is absorbed or reflected before part of it is imaged. (c) Coauthors JMP (left) and GS
(right) with BBSO/NJIT faculty Dale Gary and Bin Chen in the dome.
Fig. 3. Sample image from the Big Bear Solar Observatory’s
transit of Mercury observations, using adaptive optics. We see
the Texas-sized solar granulation on the solar photosphere in
the background of Mercury’s opaque disk. Photo credit: Jay
Pasachoff, Glenn Schneider, Dale Gary, Vasyl Vurchyshyn, and
Bin Chen of the Big Bear Solar Observatory, New Jersey Institute
of Technology.
1700 UTC (Coordinated Universal Time), BG photographed
the transit from Germany through an H-alpha filter. The
hope that simultaneous images could be found from an extreme southern site, such as South Africa, was not, however,
fulfilled. Amateur astronomers in the Republic of South Africa responded with friendly answers and also a few pictures,
but the resolution both spatially and temporally was not sufficient for the measurement.
However, two of us (JMP and GS) were using not only
small telescopes (see Fig. 1 for a sample image) but also, and
especially, a huge professional solar telescope: the 1.6-m
off-axis reflecting New Solar Telescope of the Big Bear Solar
Observatory (BBSO) of the New Jersey Institute of Technology (Latitude: 34° 15.505' N, Longitude: 116° 55.278' W). It
is on a small artificial island off the shore of Big Bear Lake,
California, with the center of the telescope’s mirror at an altitude of 2067 m (6783 ft) in the mountains about two hours
east of Pasadena and Los Angeles. (It is shown in Fig. 2.) Its
mid-water location was chosen in the 1960s by solar-physicist
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THE PHYSICS TEACHER ◆ Vol. 55, M ARCH 2017
Harold Zirin of Caltech to provide steady air even at midday
for solar observing.
Finally, we were able to use observations in a limitedwavelength band of visible light with the big telescope in
California to compare with near-simultaneous observations
taken in Germany. From 17:00 UTC onward, the filter on the
German telescope was changed to a broad visual filter from
an H-alpha filter.12 The goal was to map the photospheric
granulation as Mercury passed over it. The image used is the
result of a video seque-nce made through a broadband red
filter from 16:29:30 to 16:29:40, with a mean of 16:29:35; it is
made from the 88 images with best seeing out of the sequence
of 280 images.13
Though first contact, when Mercury’s silhouette first
touched the solar disk, was not visible from California, from
13:00 UTC onward, when the Sun rose in California, the
planet was viewable, and it rose high enough to be viewed
with the BBSO telescope at about 15:00 UTC. Mercury was
also seen in transit from Germany, and we hoped that comparison of simultaneous images would allow the parallax shift
of simultaneous pairs of Mercury images to be measured.
(Mercury had entered the solar disk from 11:12:19 to 11:15:31
UTC geocentric, passed mid-transit at 14:57:26 geocentric,
and departed the solar disk from 18:39:14 to 18:42:26 UTC
geocentric.14)
Indeed, we are able to use a series of CCD observations
(made also into a video) that was taken at the Big Bear Solar
Observatory (BBSO) (Fig. 3).15 Two of us arranged the observations in collaboration with BBSO personnel Dale Gary, Bin
Chen, Claude Plymate, Vasy Vurchyshyn, and John Varsik.
The continuum observations were taken in the TiO band
(705.7 nm, 10-Å bandpass).
For the measurement, we used both BBSO and German
images from 16:29:35 UTC. Of course, the limiting spatial
resolution from Germany was much worse, since those images were taken with only a small amateur telescope com-
angular size of Mercury as measured
from the two images resampled to a
common pixel scale.
The distance between the sites in
Weiden, in Germany, and Big Bear
Solar Observatory in California,
measured along the surface of Earth,
was determined to be 9416 km, or
a shorter 8587.7 km in space pointFig. 4. Images at relatively low resolution (left) could be easily aligned with contemporaneous
to-point
[see Fig. 6(a)]. This value
high-resolution images from the Big Bear Solar Observatory 1.6-m telescope observations
(center), by correlating patterns in the background solar granulation, to reveal the offset in the would correspond to the direction of
positions of Mercury from the two different positions on Earth.
the Sun if it were at the same angular
distance above the horizon at both
locations. However, the German measurements were with the
Sun 19.35° above the horizon while the BBSO measurements
were made with the Sun 43.7° above the horizon. The difference of 24.35° shortens the line of sight from the perspective
of the Sun to cos (24.35°)*8587.7 = 7824 km (Fig. 6).
We can then use the parallactic shift we measured as 8.86
arcseconds with the terrestrial baseline difference of 7824 to
compute the solar distance.
Parallax and the calculation of distance
Fig 5. The difference in resolution is visible between the small
telescope in Weiden, Germany (top), and the large telescope of
the Big Bear Solar Observatory (bottom) for Mercury’s silhouette,
but alignment on the granulation was easy, since the images
were taken simultaneously so the displacement was small. The
difference is 132 pixels, compared with Mercury’s diameter of 180
pixels. (Disk centers were measured, in x-y by pixels, at 4877/355
for Weiden and 479/487 for Big Bear.)
Astronomers often define distances in terms of an angle
of parallax. For example, the parallax of the Sun corresponds
to the half-angle subtended by Earth’s disk from the point
of view of an observer at the center of the Sun. (For stellar
distances, stellar parallaxes are the half-angle subtended by
the radius of the Earth’s orbit as seen from the star, and are
all less than one second of arc, preventing them from being
measured until the 19th century.) The difference between the
parallax measured from the center of the Sun and the parallactic shift measured with respect to the solar photosphere is
small (for Mercury at the center of the solar disk, ~700,000
km for the solar radius divided by ~150,000,000 km for the
solar distance = ~7/15% = ~0.5%).
Given our measured solar parallax at the UTC of the transit, specifically at the time of the images we used, as 8.86 arcseconds, using the diameter of 12,757 km for Earth, we can
pared with the Big Bear Solar Observatory’s large professional
telescope, additionally improving image fidelity at BBSO
with adaptive optics. Nevertheless, the displacement of Mercury’s image was so small
against the background
granulation that the two
images are convincingly
aligned and overlain by
inspection (as shown in
Figs. 4 and 5).
From Fig. 5, we measured the relative displacement (parallactic
shift) of the location of
Mercury with respect to
(b)
(a)
the solar photosphere as
seen from our two differ- Fig. 6. (a) To calculate the astronomical unit using the concept of parallax, we use a long, skinny triangle
ent locations on Earth.
having a baseline of the distance between two locations on Earth and perpendicular to the direction to the
Sun. (b) The baseline for the calculation is the distance between two locations on Earth and perpendicular
We compared the offset
of the two disks with the to the direction to the Sun.
THE PHYSICS TEACHER ◆ Vol. 55, M ARCH 2017
139
Exoplanet analogues
Fig. 7. Determination of the Earth-Sun distance at the time of the
transit, using the concept of parallax with a long, skinny triangle
having a baseline of the distance between two locations on Earth,
a key point being that the parallax angle is, of course, equal to the
left and to the right of the vertex at Mercury. (The diagram is not
to scale; at the right, the actual displacement is a small fraction
of the solar diameter, but it is greatly exaggerated here for clarity.)
This paper uses Kepler’s third law (1618) to relate the
distance to Mercury and the distance to the Sun, so it is a
21st-century tribute to Kepler’s work. The method of detecting planetary transits, first calculated from Johannes Kepler’s
Rudolphine Tables (1627) and using Kepler’s laws for interpretation led to NASA’s naming a planet-hunting satellite Kepler,
now in the K2 version of its extended mission. The Kepler/K2
missions have discovered thousands of exoplanets, planets
around other stars, by the transit method.19,20
Summary
We have used simultaneous measurements made at opposite sides of Earth during the 2016 transit of Mercury across
the face of the Sun to measure the apparent displacement of
the planet’s silhouette against the visible solar granulation.
We used that angular displacement to calculate the distance
at that moment between Earth and the Sun (actually, the solar
photosphere).
now calculate the distance of Earth from the Sun at that date
and time directly from the solar parallax (Fig. 7).
Though we calculated the angle for the projected distance
between our two terrestrial sites, as shown in the proportions
in the equation in the figure, the solar parallax is defined as
the angle subtended by the Earth’s radius from the Sun, which
Acknowledgments
corresponds to the views from opposite sides of the Earth
We acknowledge the collaboration at the Big Bear Solar Obdivided by two to give the terrestrial radius. So the Earth-Sun
servatory of its faculty and staff, including Dale Gary, Bin
distance = diameter of the Earth / tan [(measured solar parChen, Claude Plymate, Vasyl Vurchyshyn, and John Varsik.
allax in arcseconds/ 3600) * 2]. The result is a value of 148.5
We were pleased to have Robert Lucas (Sydney) and Evan
million km to the photosphere, or ~148.9 million km to the
Zucker (San Diego) join us for transit observations. We
solar center, for which the solar parallax is officially defined.
thank Udo Backhaus of Universität Duisberg-Essen, GerThe International Astronomical Union defines the astromany, for his comments.
nomical unit, which is approximately the average distance
from Earth to the Sun, and in 2015 they changed its notaReferences
tion from AU to au.16 To determine the astronomical unit
1. N. Pasachoff and J. M. Pasachoff, “Kepler,” in The Scientists: An
Epic of Discovery, edited by Andrew Robinson (Thames and
in linear units like kilometers, we first calculate the distance
Hudson, London, 2012), pp. 26–31.
from Mercury to the Sun in au, using the orbital period and
2.
J.
Voelkel, Johannes Kepler and the New Astronomy (Oxford
Kepler’s third law. The orbit of Mercury, however, is highly
University
Press, New York, 2000), pp. 131–132.
(with respect to that of other planets) elliptical. Therefore,
3.
J.
M.
Pasachoff
and A. Filippenko, The Cosmos: Astronomy in
the actual distance is variable. For simplicity we used a value
the
New
Millennium,
4th ed. (Cambridge University Press, New
from the PC/Mac/Linux planetarium program Cartes du Ciel
York, 2014).
(http://www.ap-i.net/skychart/en/; note hyphen in “ap-i”; it
4. O. Gingerich, “Transits in the seventeenth century and the
is not to be confused with the international effort Carte du
credentialing of Keplerian astronomy,” J. Hist. Astr. 44 (3),
17
Ciel begun in the 19th century). Accordingly, the distance
303–312 (2013).
from the center of the Sun to Mercury on the day and time of
5. J. M. Pasachoff, “Catch a pass! (of Venus with the Sun),” Odysthe simultaneous transit observations in Weiden and Big Bear
sey, 40-42 (May/June 2011).
was 0.4529 au.18
6. J. Westfall and W. Sheehan, Celestial Shadows: Eclipses, Transits,
Because of Earth’s elliptical orbit, the distance to the Sun
and Occultations (Springer, New York, 2015).
on the day of the transit was larger than the astronomical unit
7. J. M. Pasachoff, “Transit of Venus: Last chance from Earth until
of 149.6 million km; it was 1.0097 au or 151,050,000 km. Our
2117,” Phys. World 25 (5), 36–41 (May 2012).
value is therefore (151.05 – 148.9) million km = 2.15 million
8.
http://eclipsewise.com/oh/tm2016.html .
km, or about 2.15/151 = <2% from the known value.
9. G. Schneider, J. M. Pasachoff, and L. Golub, “TRACE ObservaWe attribute the uncertainty mainly to the measurement
tions of the 15 November 1999 transit of Mercury and the black
error in the observational determination of the displacement
drop effect: Considerations for the 2004 Transit of Venus,” Icarus 168, 249–256 (2004).
of Mercury’s silhouette between the two images.
10. J. M. Pasachoff, G. Schneider, and L. Golub, “The black-drop
A similar comparison was made at the 2004 transit of Veeffect explained,” in Transits of Venus: New Views of the Solar
nus between Munich and Hong Kong: http://www.astrode.de/
System and Galaxy, IAU Colloquium No. 196, edited by D. W.
venustr2.htm. See also the parallax measurements organized
Kurtz and G. E. Bromage (Cambridge University Press, Presby Udo Backhaus of Universität Duisberg-Essen, Germany, in
ton, Lankashire, U.K., 2005), pp. 242–253.
which we collaborated: http://www.venus2012.de/transit-ofmercury2016/results.php.
140
THE PHYSICS TEACHER ◆ Vol. 55, M ARCH 2017
11. J. K. Faherty, D. R. Rodriguez, and S. T. Miller, “Te Hetu’u
Global Network: Measuring the distance to the Sun using the
June 5th/6th transit of Venus,” Astr. Educ. Rev. 11 (1), (Dec.
2012); http://portico.org/stable?au=pgg3ztfbrn3. See also
https://arxiv.org/abs/1210.0873. Prof. Udo Backaus’s project
page at http://www.venus2012.de/venusprojects/contacttimes/
contacttimes.php discusses the method using contact times
instead of the parallax that is the subject of the current paper.
12. An 800 mm f/15 refractor two-element acromat was used with
a Herschel wedge to diminish the solar brightness. The Weiden site was at latitude 49.6744° and longitude 12.1489°.
13. The camera was an Omegon Proteus 120 MSI (Aptina
MT9M034 Chip).
14. F. Espenak, http://eclipsewise.com/oh/tm2016.html .
15. http://www.bbso.njit.edu/scinews/AIA_NST_Mercury_
Transit_with_title.mp4 .
16. According to its definition adopted by the XXVIIIth General
Assembly of the IAU (IAU 2012 Resolution B2), the astronomical unit is a conventional unit of length equal to 149 597
870 700 m exactly.
17. JPL’s Horizons ephemeris with DE431mx gives the same value;
http://ssd.jpl.nasa.gov/?horizons, with calculations at http://
ssd.jpl.nasa.gov/horizons.cgi.
18. Anyone interested in the calculation according to Kepler can look at the website http://www.astrode.de/
merkurtransit/5merkurt9be.htm, available in both German
and English. For a more detailed calculation of the distance to
the Sun, thanks to Prof. Udo Backhaus, see the “2016 transit of
Mercury” section of http://transitofvenus.info.
19. J. M. Pasachoff, audio tours at Smithsonian’s National Air and
Space Museum: “What did Johannes Kepler find out about
planetary orbits?” (#3); “How do astronomers today use Johannes Kepler’s findings about planetary orbits?” (#48), http://
airandspace.si.edu/exhibitions/explore-the-universe/audiotour/index.cfm, or s.si.edu/ETUaudio; transcript: http://
airandspace.si.edu/files/pdf/exhibitions/etu-audio-transcript.
pdf (2015).
20. G. Schneider, J. M. Pasachoff, and
R. C. Willson, “The effect of the
transit of Venus on ACRIM’s total
solar irradiance measurements:
Implications for transit studies of
Helium gas tube
extrasolar planets,” Astrophys. J.
emission lines
641, 565–571 (2006).
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Seeing Light in a Whole New Way
Jay Pasachoff is an astronomer at Williams
College; the observations were made and
this paper was written during a sabbatical
at Caltech. Bernd Gährken is a weekend
astronomer who organized the worldwide
effort. Glenn Schneider is an astronomer
at The University of Arizona. Pasachoff
and Schneider have studied four transits
of Mercury and two of Venus as seen
from Earth, and explained the cause of
the black-drop effect. jay.m.pasachoff@
williams.edu; [email protected];
[email protected]; http://www.
sternwarte-muenchen.de/portrait_e.
html; see http://www.astrode.de/
merkurtransit/5merkurt9be.htm
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